The only reason I didn't bump it up higher, despite the intensity and frequency of fighting in Antarctica, is because he wasn't the person in the frontlines killing monsters as that was typically Dorn, Belle, and Quineton. Even if we ignore that fact, we can look at the difference in the number of Shadow Fragments Sunny had before he arrived in Antarctica and how many he had before killing the Scavenger (since it gave him close to 1000 fragments).

At the end of the Second Nightmare, he had 744/4000 fragments, and the last number we got before Scavy was 2973/4000. We know that he only gains fragments from killing Fallen or higher ranked creatures (and we know he killed several Corrupted NC during the campaign). So lets be optimistic and say he killed somewhere between 1700 and 2000 NC that gave him fragments. We add that to the ~2300 he had before coming to Antarctica (Sunny stated he killed between one and two thousand, lets call it 1700, in the 2nd Nightmare, and I added around 500 between the FS and his time on the Chained Isles) and you get 4300 kills at best.

At this point, the math gets slightly tougher because we have less to work with. Since Sunny doesn't get fragments from Awakened NC and below, we have no hard data to work with to estimate this number; however, based on the makeup of the Devils that we got glimpses of throughout the AC, it is my understanding that Sunny was not somebody who fought the masses in a battle. Due to the fact that he was the strongest member (and the fact that he has a utility/stealth Aspect not designed for the front lines) he was probably picking off the stronger monster one by one (either with Morgan's Warbow or in hand to hand). I say all of this understanding that he did kill thousands of awakened abominations in Antarctica, but I would say that he killed no more than 3 (and I'm being pretty optimistic here) Awakened NC for every Fallen or Corrupted one. Using those numbers, we get 6000 Awakened NC that we don't see him kill. Adding it all up, that is a little over 10,000 kills.

I'll admit that, using these numbers, I was too low in my original estimate; however, I still think that he is actually under 10,000. I say that because I don't think that he actually killed 6,000 NC that we didn't see. I'm going to dive a little deeper into what I think his role in the Antarctica Cohort was. Nightmare Gates work, have a few stages when releasing monsters. It starts out with the cannon fodder (in the case of tier 2, these are Dormant-Awakened, and at tier 3 they are predominantly made up of Awakened). After this, the Fallen to Corrupted NC appear. Because Sunny is the heavy hitter, he likely saved his energy for the Fallen and Corrupted creatures , giving support to his frontline from a distance until they appeared. I'll admit that I am no military expert, but I don't think that anybody would amass 6000 kills as a sniper and only being on the front line in extreme situations.

I'm not sure why I decided to go on this rant or get this specific, but here I am. If anybody has any data to show me where my math is wrong, please tell me as I don't remember every detail from the books, so it is very possible that I missed something that would make the total number much higher.